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labwork [276]
2 years ago
13

What is the slope-intercept form of an equation of a line that passes through the point (0,-1) and is perpendicular to 5x-y=3?

Mathematics
1 answer:
Leona [35]2 years ago
8 0

Answer:

y = -1/5x - 1

Step-by-step explanation:

Perpendicular lines slopes are negative reciprocals of each other.

Write the given equation in the slope-intercept form: y = mx + b

5x - y = 3

-y = -5x + 3

y = 5x - 3       multiply by -1

The slope of the given line is 5 ( the coefficient of the x-term).

The slope of the new equation will -1/5 (this is the negative reciprocal of 5).

Next find "b"  using y = mx + b, the new slope -1/5 and the point (0, -1)

y = mx + b

-1 = -1/5(0) + b

-1 = 0 + b

-1 = b  

Now write the equation y = -1/5x - 1

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The kittens, Annie and Josie, are pushing a ball, Annie with a force magnitude of 80 N in a direction of 133 degrees, and Josie
kvv77 [185]

Answer: Then the magnitude of the force is 37.86N, and the direction is 54.35°

Step-by-step explanation:

We can write the forces as vectors.

We know that Annie pushes with a magnitude of 80N in a direction of 133° (Remember that the angles are always measured from the x-axis)

The components of this force, (Ax, Ay), are then:

Ax = 80N*cos(133°)

Ay = 80N*sin(133°)

And we know that Josie pushes with a magnitude of 95N in direction of 290°

The components of this force, (Jx, Jy), are:

Jx = 95N*cos(290°)

Jy = 95N*sin(290°)

When we add these forces, the total force acting on the ball is:

F = (80N*cos(133°) ,  80N*sin(133°)) + (95N*cos(290°), 95N*sin(290°))

F = (80N*cos(133°) + 95N*cos(290°), 80N*sin(133°) + 95N*sin(290°))

Now, the third kitten wants to do a force K, in a direction θ, such that the net force acting on the ball is zero.

Then we must have that, each component of the force of the third cat (K*cos(θ)  on the x-axis and k*sin(θ) on the y-axis), is such that:

K*cos(θ) + 80N*cos(133°) + 95N*cos(290°) = 0

k*sin(θ)  + 80N*sin(133°) + 95N*sin(290°) = 0

Now we need to solve that system for k and θ

if we simplify the equations we get:

k*cos(θ) - 22.07N = 0

k*sin(θ)  -30.76N  = 0

Now we can rewrite them as:

k*cos(θ) = 22.07N

k*sin(θ)   = 30.76N  

Now we can take the quotiet between both equations to get:

(k*sin(θ))/(k*cos(θ)) = 30.76N/22.07N

Tan(θ) = 1.394

θ = Atan(1.394) = 54.35°

Now that we know the angle, we can find the value of the magnitude k, by using one of the two equations of the system:

k*cos(54.35°) = 22.07N

k = 22.07N/cos(54.35°) = 37.86N

Then the magnitude of this force is 37.86N, and the direction is 54.35°

7 0
2 years ago
If you answered 18 questions correct on a 30 question test, what is your score?
saveliy_v [14]

Answer:

60%

Step-by-step explanation:

30/10=3

18/3=6

60%

4 0
3 years ago
What is the solution set of 7x 2 + 3x = 0? {0, 3/7} {0, -3/7} {0, -4/7}
34kurt
X(7x+3)=0
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or
7x=-3
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so,
(0,0) or (-3/7,0)
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lesya692 [45]
The answer is 2+2=4
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In standard form it would be 2,603,102. In expanded form it would be 2,000,000+600,000+3,000+100+2.
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